Schroedinger's principle eliminates the EPR-locality paradox

We introduce a principle, implicitly contained in Schroedinger’s paper (Schr35), which allows a proof of the non-existence of the EPR-locality paradox in the Copenhagen interpretation of quantum mechanics. The paradox is shown to be well-posed already in the simplest example of an entangled state of two spins one-half, independently of the (well-taken) objections by Araki and Yanase that the measurement of spin is not a local measurement. We assume that any measurement results in the collapse of the wave-packet.

💡 Research Summary

The paper by W. F. Wreszinski revisits the famous Einstein‑Podolsky‑Rosen (EPR) locality paradox and argues that, within the Copenhagen interpretation, the paradox does not actually arise once a principle implicitly contained in Schrödinger’s 1935 work is made explicit. The author calls this “Schrödinger’s principle”: after two quantum systems have interacted and become entangled, even if they are later completely separated, they can no longer be described by individual wave‑functions; only the joint wave‑function of the combined system remains a complete description.

The manuscript begins with a concise review of the standard quantum‑mechanical framework: states are vectors (or density matrices) in a Hilbert space, observables are self‑adjoint operators, and the algebra of observables for a finite region Λ is B(H_Λ) with H_Λ = ⊗_{x∈Λ} ℂ²_x. Product states, separable states, and entangled states are defined in the usual way, and the Bell singlet (Ψ_B⁻) is introduced as the prototypical entangled state of two spin‑½ particles.

A central technical tool is the Lieb‑Robinson bound for quantum spin systems, which guarantees a finite group velocity v_g that limits the speed at which any disturbance can propagate through the lattice. This bound is used to formalize the idea that information cannot travel faster than v_g, independently of the relativistic speed of light.

The EPR paradox is then restated in the language of the singlet state: Alice measures σ₃ on particle 2, obtains a definite outcome, and, according to the original EPR argument, can instantly infer the outcome that Bob will obtain when measuring σ₃ on particle 1, even if the two parties are spacelike separated. The paper introduces two explicit assumptions: (1) a measurement takes a finite time T (citing Wreszinski 2023), and (2) the measurement induces an instantaneous collapse of the wave‑packet. Combining these with the Lieb‑Robinson bound, the author shows that if the spatial separation d exceeds v_g · T, Bob’s measurement cannot be causally influenced by Alice’s result; therefore the “instantaneous remote influence” postulated by EPR is physically impossible.

The crucial step is the application of Schrödinger’s principle. When Alice obtains, say, “spin up” on her particle, the joint state collapses from the singlet to |−⟩₁⊗|+⟩₂. This collapse is a global operation on the two‑particle system, not a local operation on Alice’s subsystem alone. Consequently, Alice’s knowledge that Bob will obtain “spin down” is not the result of a superluminal signal but a logical consequence of the already‑collapsed global state. The paradox disappears because the inference does not require any new information to travel between the parties; it is already encoded in the entangled state and revealed by the global collapse.

The author contrasts this view with earlier objections. Araki and Yanase argued that spin measurements are intrinsically non‑local; however, if measurements are treated as operations on the whole entangled system, the apparent non‑locality is merely a reflection of the entangled structure, not a violation of locality. The paper also acknowledges Haag’s algebraic approach and the work of Fewster‑Versch on measurement in quantum field theory, noting that these frameworks reach the same conclusion but often hide the essential role of wave‑function collapse behind more abstract language.

In the concluding section, Wreszinski emphasizes that the EPR paradox rests on an implicit assumption of instantaneous, action‑at‑a‑distance inference, which is incompatible with both the finite measurement time and the Lieb‑Robinson bound. By adopting Schrödinger’s principle together with the Copenhagen postulate of collapse, the paradox is resolved without invoking hidden variables or alternative interpretations. The result has practical implications for quantum information and communication protocols: experimental designs must treat measurements as global collapse processes and respect the finite propagation speed dictated by Lieb‑Robinson bounds. In summary, the paper provides a clear, mathematically grounded argument that the EPR‑locality paradox does not survive a careful analysis within standard quantum mechanics, thereby reinforcing the internal consistency of the Copenhagen interpretation.